Coleman was named as the new coach of the national team this week following the shock death of Gary Speed last year.
"Craig came back for Gary, I understand that, not for me," said Coleman. "I hope he will stay, I hope that's the case.
"I will try and talk him round. I need to speak to him first.
"We need Craig Bellamy, not just because of his ability but also because of his mentality, he can be demanding and difficult but also he wants things done right and sometimes that pushes people in the right direction, so I hope he stays, I will have that conversation with him."
Coleman will take a background role when Wales face Costa Rica next month in a Gary Speed memorial match.